If the domain of f(x) is [-5,8], what is the domain of the function y = f(x+2) -1 ?
a) [-7,6]
b) [-3,9]
c) [-4,6]
d) [-7,7]
e) [-3,10]

i figured that the answer was d, however the answer key states that it is a. can you explain why?

The domain of function f(x) is [-5,8]. So no matter what the input to "f" is, the domain still applies. 
In this case the input is "x+2", set input equal to domain to solve for x.
These x values will represent new domain for f(x+2) -1.

x+2 = -5   >  x = -5 -2 = -7
x+2 = 8   > x = 8 -2 = 6

Therefore domain is [-7,6]